few_shots: Example:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Thought: This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.
Answer: C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000674

5
options: Write, read, and evaluate expressions in which letters stand for numbers.

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Write and evaluate numerical expressions involving whole-number exponents.

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
problem_activity: Activity
In this activity, students first encounter exponential expressions with variables.
Launch
Recall with students that when we write
\(6x^2\)
, we mean to multiply 6 by the result of
\(x^2\)
. Remind them that the number part of such a product is called the
coefficient
of the expression, so in this example, 6 is the coefficient of
\(x^2\)
.
Give students 5 minutes of quiet work time to evaluate the expressions. Follow with whole-class discussion.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts. After students have evaluated the first 2-3 expressions, check-in with either select groups of students or the whole class. Invite students to share the strategies they have used so far as well as any questions they have before continuing.
Supports accessibility for: Organization; Attention
Student Facing
Evaluate each expression for the given value of
\(x\)
.
\(3x^2\)
when
\(x\)
is 10
\(3x^2\)
when
\(x\)
is
\(\frac19\)
\(\frac{x^3}{4}\)
when
\(x\)
is 4
\(\frac{x^3}{4}\)
when
\(x\)
is
\(\frac12\)
\(9+x^7\)
when
\(x\)
is 1
\(9+x^7\)
when
\(x\)
is
\(\frac12\)
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may use the wrong order when evaluating expressions, such as in multiplying by 3 first in
\(3x^2\)
and then squaring. Have them recall the last lesson where they practiced applying the agreed on order of operations in numeric expressions.
Students may interpret an expression like
\(3x\)
as meaning 3 next to the digit
\(x\)
instead of as multiplication. For example, students may think that
\(3x\)
means 35 instead of 15 when
\(x=5\)
. Discuss how the shorthand notation of coefficients next to variables with no symbols between them tells us to multiply, and that it will simplify future work with expressions and equations.
Activity Synthesis
The purpose of the discussion is to ensure that students understand how to evaluate expressions with variables for a given value of the variable. It is also an opportunity for students to practice interpreting and using vocabulary like
coefficient, variable,
power,
and
exponent
.
Some guiding questions:
"In each expression, what is the coefficient?" (3, 3,
\(\frac14\)
,
\(\frac14\)
, 1, 1.)
"Choose one of the expressions. Describe the steps that you carried out to evaluate the expression." (Sample response: I rewrote
\(9+x^7\)
as
\(9+\left(\frac12\right)^7\)
. I needed to first evaluate the exponent. I knew that
\(\left(\frac12\right)^7\)
means
\(\frac12 \boldcdot \frac12 \boldcdot \frac12 \boldcdot \frac12 \boldcdot \frac12 \boldcdot \frac12 \boldcdot \frac12\)
, which is
\(\frac{1}{128}\)
. So then I wrote
\(9 + \frac{1}{128}\)
, which can also be written
\(9\frac{1}{128}\)
.
"How is evaluating the expressions when
\(x\)
is a fraction similar to when
\(x\)
is a whole number?  How is it different?" (It's similar because you're still just multiplying
\(x\)
by itself a certain number of times. It's different because multiplying a fraction by a fraction is a bit more complicated than multiplying a whole number by itself.)
Speaking, Writing: MLR8 Discussion supports.
Use this to amplify mathematical uses of language to communicate about how to evaluate exponential expressions. Revoice the term “coefficient” during student discussion and press for detail when identifying the coefficients and the order in which they are multiplied in each expression.
Design Principle(s): Support sense-making


correct_option_index: 0

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